Note that the wavevector \({\bf k}_\parallel \)  still covers the entire reciprocal space, so that both evanescent and propagating waves are considered. As we are more interested here into waves propagating in the far field, let us select a propagating wave with wavevector \({\bf k}_\text{s}=k_\text{b}\hat{\bf k}_\text{s}\)  and consider a plane above the particle, \(z>z_j\) . We therefore use \({\kappa }^+ = [{\bf k}_{\text{s},\parallel },+k_{\text{s},z}]\) . For waves propagating in the far field, we can further introduce the vector scattering amplitude, a classical quantity in scattering theory [1]}Important quantities, notably the extinction cross-section and differential scattering cross-section, can be calculated directly from the scattering amplitude.,
\({\bf f}_j(\hat{\bf k}_\text{s},\hat{\bf k}_\text{i}) = \frac{1}{4\pi } \left[ {\bf I}- \hat{\bf k}_\text{s}\otimes \hat{\bf k}_\text{s}\right] {\bf T}_j (k_\text{b}\hat{\bf k}_\text{s},k_\text{b}\hat{\bf k}_\text{i}). \) 
